For illustrating control techniques of poly-phase electrical loads, reference will be made to a star connected three-phase electrical motor in view of its large use in innumerable applications, but the same considerations apply, to any poly-phase electrical load in any configuration. One of the most widely used techniques for the control of three-phase electric motors is the FOC (Field Oriented Control). This technique is based on so-called SVM modulation (Space Vector Modulation), which induces sinusoidal voltages and currents in the windings of the motor and requires an accurate measurement of the rotor position and of the phase currents of the motor.
FIG. 1 depicts a block diagram of a system for controlling the motor torque by the FOC technique. When the windings of the motor are connected in star configuration, it is sufficient to measure only two phase currents for reconstructing the values of all three-phase currents.
When using an inverter for driving the windings of a motor, inevitably voltage harmonics superposed on the main voltage frequency are generated. These drive voltage harmonics produce current harmonics that disturb the measurement of the current in the windings.
In order to prevent or reduce spurious effects due to current harmonics, the currents are measured at certain instants. It has been shown in the article by J. Richardson entitled “Implementation of a PWM Regular Sampling Strategy for AC Drives” that there is no contribution of harmonics superposed on the main component of the current at the beginning (instant 0) and at half (T/2) of the modulation period T. As an alternative, a method that contemplates repeated current measurements during the same period for estimating the values at instants 0 and T/2 as integral average values for the modulation period is known from the article by V. Blasko, et al. entitled “Sampling Methods for Discontinuous Voltage and Current Signals and Their Influence on Bandwidth of Control Loops of Electrical Drives”.
In general, measurement of phase currents for controlling a three-phase electric motor through an inverter contemplates the use of at least two current sensors coupled to the motor windings. Moreover, in order to protect the system from eventual overcurrents and/or overvoltages, another sensor, typically a sensing resistor, is connected on a so-called DC-LINK line, as depicted in FIG. 2. Therefore, a total of three current sensors are generally required.
In order to reduce the number of current sensors and thus overall costs, and to increase efficiency, the sensors connected to the phase windings of the load may not be employed and the current sensor placed on the DC-LINK line be exploited also for measuring the phase currents. Indeed, considering the possible states of a three-phase inverter, it is noticed that, depending on the state of the switches, the current flowing through the DC-LINK line is null or equal in amplitude to one of the phase currents of the motor, as shown in following table.
Voltage vectorsDC-link100ia110−ic010+ib011−ia001+ic101−ib000-111 (unused)0
By carrying out at most four current measurements per modulation period, it is thus possible to estimate two of the three phase currents of the motor at the instants 0 and T/2 of the modulation period T. For example −ic and ia can be calculated for the same instant T/2, as the mean value of ic1 and ic2 and of ia1 and ia2, respectively, as shown in FIG. 3. The figure shows a modulation pattern, waveforms of the current flowing through the line DC-LINK, and the instants at which the current measurements are carried out.
As stated above, in order to reduce as much as possible contributions due to harmonics (caused by the inverter), the currents should be measured at the instants 0 and T/2 of the modulation period T. By exploiting the symmetry of the modulation pattern, it is possible to obtain the value of currents at the instant T/2 as the mean value of the two current measurements mode at the instants 0. This estimation is substantially free of inaccuracies due to harmonics.
Nevertheless, this technique is burdened by problems due to the modulation pattern. When the voltage vector to be applied to the phase windings of the motor is near the border between two possible sectors of the pattern (dashed zone in FIG. 4(a)), only one current can be measured correctly, but not the other. Indeed, the available time window within which the measurement can be done is so short that it does not allow a correct measurement by an A/D converter as commonly employed. In particular, by neglecting the ringing phenomena due to state transitions of the inverter, the time window should last at least the sampling time of the converter.
Moreover, if a single A/D converter is used, the time interval between the beginning of two useful measurement windows should be at least longer than or equal to the conversion time. A similar problem arises in conditions of small modulation indices (FIGS. 4 (c) and (d)): in these cases it is impossible to measure any of the phase currents of the motor.
In order to overcome the above problems, two methods are known from the article by Woo-Cheol Lee et al. entitled, “Comparison of Single-Sensor Current Control in the DC Link for Three-Phase Voltage-Source PWM Converters”. The functioning principle on which they are based is the same, but they work differently. The first method, illustrated in FIG. 5, contemplates an arrangement of the voltage vector components that substantially determines a time shift of the active intervals of the involved PWM signals. This method keeps the time duration of the active interval for each PWM signal (this is a necessary condition for not altering the driving of the motor) and does not increase the number of switchings and thus leaves unchanged the conduction losses.
However the modulation pattern is no longer symmetrical, thus the total harmonic distortion (THD) of the phase currents of the motor increases. Moreover, it is impossible to carry out symmetric measurements of both currents and to calculate current values at the same instant, thus it is impossible to eliminate the error due to the current harmonics that are inevitably generated by the inverter. Moreover, this method is not applicable for driving the motor with relatively small modulation indices.
The second method, illustrated in FIG. 6, contemplates, as in the previous case, a driving that implies a time shift of the active intervals. This method keeps the time duration of the active state of each PWM signal, but increases the number of switchings when the voltage vector to be applied to the phase windings of the motor is close to the border between two sectors of the modulation pattern, thus increasing the amount of conduction losses. Moreover, in both cases (FIGS. 6 (a) and (c)) two simultaneous switchings take place and this is not desirable because it could prolong transients that follow the switchings, thus increasing the minimum time required for measurements. The modulation pattern is not symmetrical, thus the THD of the phase currents of the motor increases and it is impossible to carry out symmetrical measurements for two phase currents. Therefore, it is impossible to estimate precisely the value of two currents at the same instant and thus the error due to current harmonics superposed to the main frequency cannot be eliminated.
Indeed, it could be possible to calculate −ic and ia at the same instant T/2, no longer as the mean value of ic1 and ic2 and of ia1 and ia2−ic, respectively, but as a weighted time average. However, this procedure significantly increases the computational load because it is not sufficient to halve the sum of the values (that may be executed with a fast bit-shift operation using a very simple hardware), but it implies a division that requires a more complex hardware, and weight coefficients to be used in the time averaging operation by carrying out multiplications of coefficients and measured values.